(b)
$H_{2}^{+} = \sigma 1s^{2}\$(According to molecular orbital theory)
Bond order = $\frac{bonding\ electrons - antibonding\ electrons}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2} = 0.5$
$H_{2}^{+}$ is paramagnetic due to the presence of one unpaired electron.